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res:
bibo_abstract:
- For any n≥3, let F ∈ Z[X0,...,Xn ] be a form of degree d *≥5 that defines a non-singular
hypersurface X ⊂ Pn . The main result in this paper is a proof of the fact that
the number N (F ; B) of Q-rational points on X which have height at most B satisfiesN
(F ; B) = Od,ε,n (Bn −1+ε ), for any ε > 0. The implied constant in this estimate
depends at most upon d, ε and n. New estimates are also obtained for the number
of representations of a positive integer as the sum of three dth powers, and for
the paucity of integer solutions to equal sums of like polynomials.*@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Timothy D
foaf_name: Timothy Browning
foaf_surname: Browning
foaf_workInfoHomepage: http://www.librecat.org/personId=35827D50-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Roger
foaf_name: Heath-Brown, Roger
foaf_surname: Heath Brown
bibo_doi: 10.1112/S0024609305018412
bibo_issue: '3'
bibo_volume: 38
dct_date: 2006^xs_gYear
dct_publisher: Wiley-Blackwell@
dct_title: The density of rational points on non-singular hypersurfaces, I@
...